Question

You are wearing a pair of cargo pants with six pockets. You've put $10 in one of the pockets, but you cannot remember which one. After checking two pockets without success, what is the probability that the money will be in the next pocket you check?

Answer 1

There are 6 pockets all together.  You checked two of them and it wasn't
there.  So you can forget about those 2, and now there are 4 pockets left.

The total number of ways for your next try is 4.
The number that will be successful is 1.

The probability of success on the next one is  1/4  =  25% .

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Another method of solution, somewhat more complex:

Total number of pockets = 6.
Amount of money missing = $10
First partial sum, i.e. sum of numbers
 in the first part of the problem = 6 + 10  =  16.

Total number of pockets  =  6
Current value of cargo pants on a fashion scale from 1 to 10  =  -2.
Second partial sum =  6 - 2  =  4.

  Probability = (second partial sum) / (first partial sum) = 4/16  =  25% .